At Belfort the investing force was at first but 10,000 and the line of investment 25 miles long, giving but 400 men to the mile. This force was subsequently increased to 20,000 men, and when the besieging army had all arrived, to 32,000 men. At Paris (1870) the line of investment was about 3 miles from the line of the forts, and about 53 miles in length, the investing force 180,000, giving a mean of about 2 men to the yard. The distribution was, however, about 4 to the yard on the left bank and 1⅓ on the right bank of the Seine. At Plevna the line of investment was 2¾ miles from the forts, its length 43½ miles, the investing force 100,000 men, about 1¼ men to the yard. In each of these sieges the place finally fell under the attack of a force, in no case equal to 2½ times the garrison; but inferences drawn from this fact are apt to be erroneous, since none of these places was well fortified according to modern methods, well garrisoned, well supplied, and defended to extremity. The results show, however, that under similar circumstances, which are apt to arise in any modern war, the attack of a strong place which can be completely invested by a force of two or three times the strength of the garrison, may promise success; which seems to be assured if the defence allows the besieging force to complete the investment and thoroughly intrench itself. On the other hand, tactical considerations would indicate that a well-equipped army, of good morale, under an active and aggressive commander, covered by a modern intrenched camp, should be able to prevent the investment; and by taking advantage of its interior lines, its heavy guns and its strong _points d’appui_, should be able to beat in detail a force very much greater than itself whose fractions, by reason of the extent of the line of investment, are necessarily not within supporting distance of each other. These advantages of the defence evidently disappear, as above indicated, when the attack is allowed to complete its fortifications, since under their cover a small force can check even a determined sortie until a sufficient force to beat it can be concentrated. From these considerations it is evident that an investment, once completed, may be maintained by a force less than that necessary to establish it in the first place (see Investment of Plevna, Pierron, Méthodes de Guerre Vol. III, pp. 647 _et seq._).